Question
Wed September 11, 2013 By:

1. If x=3-2?2, find ?x + 1/x 2. In the figure given below, the side of triangle PQR is produced to a point S . if the bisector of angle PQR and angle PRS meet at point T, then prove that angle QTR = ½ angle QPR

Expert Reply
Wed September 11, 2013
1) x = 3 - 2?2

=> ?x = ?(3- 2 ?2)

= ?[(?2)2+ (?1)2 - (2)(?2)(?1)]

= ?(?2 - ?1)2                    [Since, a2+b2+2ab = (a+b)2]

= ?2 - ?1

 

Putting the value of ?x in the given expression, we get,

root x + 1/rootx

= (?2 - ?1) + 1/( ?2 - ?1)

= (?2 - ?1) + ( ?2 + ?1)/( ?2 - ?1)( ?2 + ?1)

= (?2 - ?1) + ( ?2 + ?1)/2-1

= (?2 - ?1) +  (?2 + ?1)

= 2?2

2) Your second question is not clear. The figure has not been uploaded properly. Please clarify so that we may answer it to the best of the ability.

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